According to the prior art, electrical potentials or electrical fields are measured at nanometer resolution using scanning probe microscopes by means of either local contact potential difference measurement (Kelvin probe force microscopy—KPFM) or direct measurement of the forces between charges in a sample and the image charges in the metal tip caused by influence (electrostatic force microscopy—EFM). (S. Sadewasser, T. Glatzel, eds. Kelvin Probe Force Microscopy. Springer Verlag Berlin Heidelberg 2012. J. Colchero, A. Gil, and A.M Baró, ‘Resolution enhancement and improved data interpretation in electrostatic force microscopy’, Physical Rev. B 64 245403 (2001).)
However, the methods according to the prior art have some drawbacks. In EFM, forces acting on parts of the atomic-force microscope tip that are located further away are also measured, since electrical fields are long-range, while in KPFM the measured contact potential different is also influenced by parts of the scanning probe microscope tip that are located further away. As a result, the size of the metal tip, in particular the tip radius, which cannot measure much below 30 nm, restricts the lateral resolution that can be attained with the particular measurement. This restriction occurs in both KPFM and EFM. A drawback of EFM is that only forces are measured—not electrical fields and potential differences —and so it is difficult to determine the electrical field since it is not possible to measure any verified, independent information on the charges influenced in the tip. A disadvantage of KPFM is that the measurement resolution is dependent on the distance from the tip to the sample being investigated and on the tip radius. For this reason, KPFM can also only be used to measure two-dimensional contact potential difference maps over a sample surface; these maps are difficult to expand into the third dimension vertically with respect to the sample surface.
In addition, the force measured by the atomic-force microscope is non-specific, so in EFM, in addition to the electrical forces to be quantitatively detected, all the other active forces, such as van der Waals forces, are detected too.
The overall force is then measured. Extracting or determining the electrical force thus necessitates complex analysis methods, if these are even possible. This is a particularly large drawback when the local electrical potential field around nanostructures is to be measured and when other forces, such as van der Waals forces, are significantly less laterally dependent on the lateral position but are possibly much stronger than the electrical force. In this case, the signal being sought has to be determined as a small modulation on a large signal, which creates measurement problems.